Covariant Inertial Forces for Spinors

TL;DR

This paper introduces covariant inertial force tensors derived from Dirac spinors interacting with electrodynamics and torsion-gravity, revealing new geometric objects that behave like inertial forces and remain non-zero even in free fields.

Contribution

It presents a novel set of covariant tensors from Dirac spinors that resemble inertial forces and are distinct from connection information, with applications to hydrogen atom states.

Findings

Invariants of these tensors are non-zero for free fields.

The tensors provide a covariant description of inertial effects.

Application to hydrogen atom demonstrates their physical relevance.

Abstract

In this paper we consider the Dirac spinor field in interaction with a background of electrodynamics and torsion-gravity; by performing the polar reduction we acquire the possibility to introduce a new set of objects that have the geometrical status of non-vanishing tensors but which seem to contain the same information of the connection: thus they appear to be describing something that seems like an inertial force but which is also essentially covariant. After a general introduction, we exemplify these tensors in the very well known instance of the orbital of minimal energy for an electron in the case of the Hydrogen atom: we will see that the invariants built with these tensors remain different from zero even for free field configurations. An outlook regarding possible interpretations of such a set of tensors will be sketched. A few final comments will eventually be given.